A fuzzy fixed-point theorem and its applications to maximal elements and Nash equilibria in noncompact CAT(0) spaces

Article type: Research Article

Authors: Lu, Haishu^{; *} | Li, Rong

Affiliations: School of Business, Jiangsu University of Technology, Changzhou, Jiangsu, P.R. China

Correspondence: [*] Corresponding author. Haishu Lu, School of Business, Jiangsu University of Technology, Changzhou 213001, Jiangsu, P.R. China. E-mail: [email protected].

Abstract: In this paper, based on the KKM method, we prove a new fuzzy fixed-point theorem in noncompact CAT(0) spaces. As applications of this fixed-point theorem, we obtain some existence theorems of fuzzy maximal element points. Finally, we utilize these fuzzy maximal element theorems to establish some new existence theorems of Nash equilibrium points for generalized fuzzy noncooperative games and fuzzy noncooperative qualitative games in noncompact CAT(0) spaces. The results obtained in this paper generalize and extend many known results in the existing literature.

Keywords: CAT(0) space, fuzzy fixed point, fuzzy maximal element, fuzzy noncooperative game, Nash equilibrium point

DOI: 10.3233/JIFS-212194

Journal: Journal of Intelligent & Fuzzy Systems, vol. 42, no. 6, pp. 6045-6062, 2022